Cardinal welfarism relies on the idea of comparison of agents' utility functions in different states of the world. Treating agents' utilities as a criteria evaluating states of the world allows to consider entire decision situation as a multi-criteria optimization problem. Such approach is devoid ethical content; the only aim is to pick Pareto-optimal solution.

Usually Pareto-optimal set consists of more than a single member, yet one decision has to be made. In order to compare those alternatives one has to formulate social welfare ordering (SWO) which is a preference relation amongst utility profile vectors of all agents. Obviously, formulated ordering has to apply certain justice principles which may differ regarding the situation we are dealing with. Basic representantive ideas which were developed through centuries are of great use:
\begin{itemize}
\item Utilitarianism
\item Egalitarianism
\item Nash collective utility function
\end{itemize}

\begin{figure}[h!tb]
    \begin{center}
	\includegraphics[scale=.6]{img/t_all}
    \caption{Comparison of basic ideas. Red curve is the Pareto-optimal frontier}
    \label{fig:cufs}
    \end{center}
\end{figure}

\subsection{Requirements on SWO}

\begin{itemize}
\item Complete and transitive
\item Monotonic - if one agent's utility increases, ceteris paribus, social welfare increases likewise %(connected with pareto-optimality - all maximum elements of monotonic SWO are pareto-optimal)
\item Symmetric - agents order doesn't make a difference - permutation over their utility index is indifferent to the basic one (equal treatment of equals)
\end{itemize}

%SUW represented by CUF (except rawls' leximin) - real valued (collective utility) function with utility profile for argument

%\item in single commodity allocation problem all feasible solutions are pareto-optimal, provided utilities aren't aggregated

%\item independence of unconcerned agents IUA - agent, whose utility doesnt alter between two profiles can be ignored. SWO focuses on agents, whose utility is affected by decision
%\item pigou-dalton transfer principle - reduce inequality between some agents, provided social welfare doesnt decrease - concavity of function $g(u)$
%\item independence of common scale ICS - scaling utilities doeasnt affect social welfare ordering, provided utilities and scaling constant are nonnegative
%\item [fair division -> p. 67-68]
%\item compensation (egalitarianism) - leximin SWF selects most egalitarian among pareto-optimal utility distributions.
%\begin{enumerate}
%\item rearrange utility profiles in ascending order
%\item compare new profiles lexicographically
%\item profile with higher utility at compared place is preferred
%\item rearranged profiles are indifferent with the basic ones due to symmetry property
%\end{enumerate}
%\item leximin cannot be represented by any CUF
%\item leximin is ICS, IUA and satisfies pigou-dalton
%\item independence of common utility pace
%\end{itemize}
%comparison - utilitarianism/nash/leximin [fair division -> p.76]


